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A body oscillates with SHM, accroding to...

A body oscillates with SHM, accroding to the equation, `x=(5.0m)cos[(2pi t+pi//4]`
At `t=1.5s`, calculate the `(a)` diplacement `(b)` speed and `(c)` acceleration of the body.

Text Solution

AI Generated Solution

To solve the problem, we will calculate the displacement, speed, and acceleration of a body oscillating in simple harmonic motion (SHM) according to the equation: \[ x = (5.0 \, \text{m}) \cos \left(2\pi t + \frac{\pi}{4}\right) \] at \( t = 1.5 \, \text{s} \). ### Step 1: Calculate Displacement ...
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Knowledge Check

  • A body oscillates with SHM according to the equation (in SHM unit ), x=5"cos"(2pit+(pi)/(4)) . Its instantaneous displacement at t=1 s is

    A
    `(sqrt(2))/(5)`m
    B
    `(1)/(sqrt(3))`m
    C
    `(1)/(2)` m
    D
    `(5)/(sqrt(2))` m

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    A
    `11.1 ms^(-1)`
    B
    `22.2 ms^(-1)`
    C
    `33.3ms^(-1)`
    D
    ` 44.4 ms^(-1)`

  • A body osicllates with SHM according to the equation x=6cos(2pit+(pi)/(4)) . Its instantaneous displacement at t = 1 sec is

    A
    `(sqrt(2))/(5)`
    B
    `(1)/(sqrt(3))`
    C
    `(1)/(sqrt(2))`
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